We study repeated games with frequent actions and frequent imperfect public signals, where the signals are aggregates of many discrete events, such as sales or tasks. The high-frequency limit of the equilibrium set depends both on the probability law governing the discrete events and on how many...

In some experiments rational players who understand the structure of the game could improve their payoff. We bound the size of the observed losses in several such experiments. To do this, we suppose that observed play resembles an equilibrium because players learn about their opponents' play....

We present a general algorithm for computing the limit, as δ → 1, of the set of payoffs of perfect public equilibria of repeated games with long-run and short-run players, allowing for the possibility that the players′ actions are not observable by their opponents. We illustrate...

We propose that a simple “dual-self†model gives a unified explanation for several empirical regularities, including the apparent time inconsistency that has motivated models of quasi-hyperbolic discounting and Rabin's paradox of risk aversion in the large and small. The model also...

The philosophy of equilibrium refinements is that the analyst, if he knows things about the structure of the game, can reject some Nash equilibria as unreasonable. The word “know†in the preceding sentence deserves special emphasis. If in a fixed game the analyst can reject a...

In a repeated game with imperfect public information, the set of equilibria depends on the way that the distribution of public signals varies with the players' actions. Recent research has focused on the case of “frequent monitoring,†where the time interval between periods becomes...

We study a variation of fictitious play, in which the probability of each action is an exponential function of that action's utility against the historical frequency of opponents' play. Regardless of the opponents' strategies, the utility received by an agent using this rule is nearly the best...

We comment on the Shoham, Powers, and Grenager survey of multi-agent learning and game theory, emphasizing that some of their categories are important for economics and others are not. We also try to correct some minor imprecisions in their discussion of the economics literature on learning in...

We provide a necessary and sufficient condition for equilibria of a game to arise as limits of ε-equilibria of games with smaller strategy spaces. As the smaller games are frequently more tractable, our result facilitates the characterization of the set of equilibria.

In a self-confirming equilibrium, each player correctly forecasts the actions that opponents will take along the equilibrium path, but may be mistaken about the way that opponents would respond to deviations. This paper develops a refinement of self-confirming equilibrium in which players use...